While Trump doesn't yet have the 1,237 delegates he needs to lock down the Republican presidential nomination, he doesn't seem to have much doubt left that he will get there.

"I consider myself the presumptive nominee, absolutely," Trump said during a speech and news conference at Trump Tower in New York City.

He said later: "As far as I'm concerned, it's over."

Trump said his rivals for the GOP nomination, Sen. Ted Cruz of Texas and Gov. John Kasich of Ohio, "should really get out of the race."

"They have no path to the nomination," he said, later adding, "They should get out of the race, and we should heal the Republican Party."

Trump insisted that he could unify a Republican Party that seems increasingly divided.

"I'm a unifier. I unify people," he said. "That's how I did it in business ... We will have people that are backing this party and backing my candidacy that you wouldn't believe. We're going to have such unity."

On Sunday, Kasich and Cruz announced an alliance to essentially halt campaigning in certain states where the other candidate has a clear advantage in an attempt to block Trump from winning the nomination.

If Trump does not reach the 1,237-delegate threshold, he could run into problems attempting to secure the nomination. Cruz has continually outmaneuvered Trump in electing delegates to the Republican National Convention. If Trump does not win 1,237 delegates, many convention delegates would become "unbound" to Trump in later rounds of convention voting, giving Cruz or Kasich a likely boost in support.